Question

given that abcd is a rectangle with ao = 4x - 3 and bo = 5x - 10, what is the value of x?

Explanation:

Step1: Recall property of rectangle

In a rectangle, the diagonals are equal and bisect each other. So \(AO = BO\).

Step2: Set up equation

Given \(AO = 4x - 3\) and \(BO = 5x - 10\), then \(4x - 3=5x - 10\).

Step3: Solve the equation

Subtract \(4x\) from both sides: \(-3=x - 10\).
Add \(10\) to both sides: \(x = 7\).

Answer:

\(x = 7\)